We are visiting Rome for several days. Can we visit churches on Sundays?
yes you can but please no photos or cell phones during mass
Visitors are discouraged from visiting during Mass (very polite signs as you enter). Most Mass times are 10-11 or 10:30-11:30 am, so if the churches you want to visit are open in the afternoon, that might be better. I find it annoying to have people walking around looking at artwork during the Mass, but some larger churches have Mass in a chapel snd the main part of the church is open to visitors.
Many museums and all archeological parks are open on Sunday morning. You might think about visiting the via Appia Antica on Sunday when it is closed to car traffic, and visiting churches in the afternoon.
Good advice above. Yes, you may visit the churches IF they have posted visiting hours on Sundays: they're all different. Some have heavy mass schedules so it can be difficult to find open (non-mass) hours in which to look around but others may only have a couple of masses a day.
And as Zoe pointed out, some have large side chapels, or have mass in their side chapels so that the main part or other sections may be visited during services without causing disruption.